Problems on Profit Loss
Q31. By selling a table for Rs. 450 instead of Rs. 500 loss percent increases by 5%. The cost price of the table is
(a) Rs. 500
(b) Rs. 850
(c) Rs. 1000
(d) Rs. 1200
Answer: (c) Rs. 1000
Let the C.P be Rs. x
1st loss % = | (x - 500) | X 100 |
x |
= | 100 (x - 500) |
x |
2nd loss % = | x - 450 | X 100 |
x |
= | 100 (x - 450) |
x |
A/Q, | 100 (x - 450) | = | 100 (x - 500) | + 5 |
x | x |
⇒ | 100 (x - 450) | - | 100 (x - 500) | = 5 |
x | x |
⇒ | 100x - 45000 - 100x + 50000 | = 5 |
x |
⇒ 5x = 5000
⇒ x = Rs. 1000
Q32. A man buys an article for 5% less than its value and sells it for 5% more than its value. His gain or loss percent is
(a) 10(10/19)%
(b) 15(5/9)%
(c) 29(12/17)%
(d) 32(12/17)%
Answer: (a) 10(10/19)%
Let the value of the article be Rs. x
∴ C.P = Rs. (x X | 95 | ) = Rs. | 19x |
100 | 20 |
S.P = Rs. (x X | 105 | ) = Rs. | 21x |
100 | 20 |
∴ Gain % = Rs. ( | 21x | - | 19x | ) = Rs. | 2x | = Rs. | x |
20 | 20 | 20 | 10 |
∴ Gain % = | x/10 | X 100 |
(19/20)x |
= | x | X | 20 | X 100 |
10 | 19x |
= | 200 | % |
19 |
= 10 | 10 | % |
19 |
Q33. The marked price of an article is 5% more then the cost price and a discount of 5% is given on the marked price. Then the loss is
(a) 0.25%
(b) 0.65%
(c) 0.72%
(d) 0.99%
Answer: (a) 0.25%
Let the C.P be Rs. 100
∴ M.P = Rs. 105
∴ S.P = 95% of Rs. 105
= (95/100) X 105 = Rs. 99.75
∴ Loss = Rs. (100 - 99.75) = 0.25%
Q34. The marked price of a radio is Rs. 2000. The shopkeeper allows a discount of 10% and gain 8%. If no discount is allowed his gain percent would be
(a) 15%
(b) 20%
(c) 27%
(d) 33%
Answer: (b) 20%
S.P = 90% of Rs. 2000 = (90/100) X 2000 = Rs. 1800
Gain = 8%
∴ C.P = Rs. (100/108) X 1800 = Rs. 1666.66
New S.P = Rs. 2000
C.P = Rs. 1666.66
∴ Gain % = (333.34/1666.66) X 100 = 20%
Q35. A trader lists his articles 10% above the C.P and allows a discount 5% on cash payment. His gain percent is
(a) 3.7%
(b) 4.1%
(c) 4.5%
(d) 5.2%
Answer: (c) 4.5%
Let the C.P be Rs. 100
∴ M.P = Rs. 110
S.P = 95% of Rs. 110
= (95/100) X 110 = Rs. 104.50
∴ Gain = Rs. (104.50 - 100) = Rs. 4.50
Gain % = 4.5%
Q36. A dealer processing to sell his goods at cost price, uses 900 gm weight for 1kg. His gain percentage is
(a) 11(1/9)%
(b) 12(1/3)%
(c) 14(1/2)%
(d) 17(1/3)%
Answer: (a) 11(1/9)%
Gain % = { | Error | X 100} % |
True value - Error |
= { | 100 | X 100} % |
1000 - 100 |
= { | 100 | X 100} % |
900 |
= 11 | 1 | % |
9 |
Q37. The selling price of an article is ¾ times its cost price. The loss percent is
(a) 25%
(b) 34%
(c) 38%
(d) 39%
Answer: (a) 25%
Let the C.P be Rs. 100
∴ S.P = Rs. 100 X (3/4) = Rs. 75
∴ Loss % = 100 - 75 = 25%
Q38. The selling price of an article is 5/4 times its cost price. The gain percent is
(a) 25%
(b) 34%
(c) 38%
(d) 39%
Answer: (a) 25%
Let the C.P be Rs. 100
∴ S.P = Rs. 100 X (5/4) = Rs. 125
∴ Gain % = 125 - 100 = 25%
Q39. On selling an article for Rs. 56, one losses 20%. In order to gain 20% what would be the selling price
(a) Rs. 47
(b) Rs. 54
(c) Rs. 62
(d) Rs. 84
Answer: (d) Rs. 84
Let the C.P be Rs. x
∴ 80% of x = 56
⇒ (80/100) X x = 56
⇒ x = (560/8) = 70
∴ C.P = Rs. 70
Gain = 20%
∴ S.P = Rs. (120/100) X 70 = Rs. 84
Q40. By selling 33m of cloth Ram gained the cost price of 11m. The gain percent is
(a) 25(1/3)%
(b) 26(1/3)%
(c) 33(1/3)%
(d) 37(1/3)%
Answer: (c) 33(1/3)%
Let the C.P of 1m cloth be Rs. x
∴ The C.P of 33m cloth be Rs. 33x
Gain = 11x
∴ Gain % = (11x/33x) X 100
= 33(1/3)%
Practice Test Exam